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Bubble dynamics in a compressible liquid. Part 1. First-order theory

Published online by Cambridge University Press:  21 April 2006

A. Prosperetti  and
A. Lezzi
A. Prosperetti
Affiliation:
Dipartimento di Fisica, Universitá degli Studi, 20133, Milano, Italy Present address: Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA.
A. Lezzi
Affiliation:
Dipartimento di Fisica, Universitá degli Studi, 20133, Milano, Italy Present address: Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Abstract

The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 168 , July 1986 , pp. 457 - 478
Copyright
© 1986 Cambridge University Press

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